[cheerful upbeat music] ♪ WELCOME TO CLASSROOM CONNECTION.

I'M YOUR HOST, MR. R., AND I'M ALSO A TEACHER.

I HOPE YOU'LL JOIN ME IN THE CLASSROOM AS WE LEARN FROM TEACHERS ALL ACROSS THIS BEAUTIFUL STATE OF NORTH CAROLINA.

♪ HI, MATHEMATICIANS.

MS. NABORS HERE AGAIN.

TODAY, WE'RE GOING TO USE A NUMBER LINE TO MODEL FRACTIONS.

YOU MAY ALREADY KNOW WHAT A NUMBER LINE LOOKS LIKE.

YOU MAY HAVE SEEN A NUMBER LINE BEFORE, LIKE THIS.

NUMBER LINES SHOW US THE DISTANCE BETWEEN NUMBERS.

FOR EXAMPLE, I CAN SEE THAT THE DISTANCE BETWEEN 1 AND 4 IS 3, BECAUSE I WOULD NEED TO MAKE 3 JUMPS AFTER 1 TO REACH 4.

BECAUSE NUMBER LINES SHOW DISTANCE, THEY'RE A GOOD TOOL TO USE WHEN LOOKING AT STORIES OR PROBLEMS INVOLVING PEOPLE TRAVELING OR MOVING.

THIS NUMBER LINE STARTS AT 1 AND ENDS AT 10.

THIS NUMBER LINE SHOWS WHOLE NUMBERS.

TODAY, WHEN WE LOOK AT FRACTIONS, WE'RE GOING TO LOOK AT A NUMBER LINE BETWEEN 0 AND 1, LIKE THIS.

CAN YOU THINK OF A TIME THAT YOU WALKED LESS THAN 1 WHOLE UNIT, LIKE A MILE?

ME TOO.

I JUST WALKED LESS THAN 1 MILE TO PICK UP MY MAIL FROM THE MAILBOX.

WELL, TODAY, WE'RE GOING TO LOOK AT A WALK-- A WALK SOMEONE NAMED ALEX WENT ON.

I'M NOT SURE IF ALEX IS A BOY OR GIRL, SO I'M GOING TO REFER TO ALEX AS "THEY" WHEN I REFERENCE THEM.

FOR EXAMPLE, I MIGHT SAY, "THEY WENT FOR A WALK AND STOPPED FOR WATER."

WHEN I SAY "THEY," I'M TALKING ABOUT ALEX.

ALEX'S WALK INVOLVES A TRAIL IN THEIR COMMUNITY.

THIS TRAIL RUNS ALONG A POND THAT'S 1 MILE LONG IN DISTANCE.

ALEX IS LEARNING ABOUT FRACTIONS, LIKE US, AND WANTS TO NAME THE DISTANCE THEY WALKED USING A FRACTION, BUT IS HAVING A LITTLE TROUBLE.

SO, WE'RE HERE TO HELP.

WE'LL USE A NUMBER LINE TO MODEL THE DISTANCE ALEX WALKED.

THE NUMBER LINE STARTS AT 0 AND ENDS AT 1.

WHY DO YOU THINK WE CAN LABEL THE NUMBER LINE LIKE THIS?

OH, I HEARD SOMEONE SAY THAT WE NEED TO START AT 0 BECAUSE IT REPRESENTS A DISTANCE OF 0, MEANING ALEX HAS NOT TRAVELED ANY DISTANCE YET.

1 REPRESENTS THE END OF THE TRAIL, BECAUSE WE KNOW THAT THE TRAIL ALEX WALKED WAS 1 MILE LONG.

I'M SO EXCITED TO FIND OUT WHAT ALEX DID ON THEIR WALK, SO, LET'S LOOK.

ARE YOU READY?

ME TOO.

IT LOOKS LIKE ALEX IS OFF AND WALKING.

OH, ALEX IS STOPPING.

LET'S CHECK IT OUT.

YEAH, IT LOOKS LIKE ALEX IS STOPPING TO TAKE A PICTURE.

I DO THAT TOO WHEN I TAKE A WALK.

DO YOU?

IT'S FUN TO TAKE PICTURES.

WHAT ARE YOU WONDERING AT THIS POINT?

LEAN IN AND WHISPER IT TO ME.

OH, ME TOO.

I HEARD SOMEONE SAY THAT THEY WONDER HOW FAR ALEX WALKED BEFORE THEY STOPPED.

WELL, IT LOOKS LIKE AFTER WALKING 1/6 OF A MILE, ALEX STOPPED TO TAKE A PICTURE OF A TURTLE.

LET'S THINK ABOUT NUMERATORS AND DENOMINATORS TO HELP US UNDERSTAND THIS AMOUNT.

WHEN WE WRITE A FRACTION, THERE ARE 2 PARTS.

DO YOU REMEMBER WHAT THEY'RE CALLED?

THAT'S RIGHT.

THE PARTS OF A FRACTION ARE CALLED THE "NUMERATOR" AND THE "DENOMINATOR."

THE NUMERATOR AND DENOMINATOR OF A FRACTION ARE SEPARATED BY A BAR.

OH, WAIT, I HEARD SOMEONE ASK A QUESTION.

SOMEONE ASKED WHAT THE NUMERATOR AND DENOMINATOR OF A FRACTION REPRESENT.

THAT'S A GREAT QUESTION.

THE DENOMINATOR IS THE BOTTOM NUMBER, AND IT REPRESENTS THE AMOUNT OF SAME-SIZE UNITS THE WHOLE WAS PARTITIONED INTO.

THE NUMERATOR IS THE TOP NUMBER, AND IT REPRESENTS THE NUMBER OF SAME-SIZE UNITS COUNTED.

LOOK AT THE FRACTION 1/6.

WHAT NUMBER IS THE DENOMINATOR?

SHOW IT TO ME BY HOLDING UP THAT NUMBER OF FINGERS.

THAT'S RIGHT.

THE DENOMINATOR 6 IS THE NUMBER OF SAME-SIZE UNITS THAT WE PARTITION INTO.

LOOKING AT THE FRACTION 1/6, IT SEEMS LIKE ALEX BROKE UP THEIR WALK INTO INTERVALS, OR UNITS, OF 6, SO, THE DENOMINATOR IS 6.

HOW ABOUT THE NUMERATOR?

SHOW ME WITH YOUR FINGERS WHAT NUMBER IS THE NUMERATOR.

YEP.

THE NUMERATOR IS 1, BECAUSE ALEX HAS ONLY TRAVELED 1/6, OR 1 INTERVAL, SO FAR, SO, WE ONLY HAVE COUNTED 1/6, AND THE NUMERATOR 1 IS HOW MANY SIXTHS WE'VE COUNTED.

GREAT JOB.

ALEX BROKE UP THEIR WALK INTO SIXTHS AND STOPPED AT DIFFERENT INTERVALS, OR PARTS, TO DO CERTAIN THINGS.

YOU MAY HAVE WORKED IN THE PAST TO PARTITION SHAPES.

TODAY, WE'RE PARTITIONING NUMBER LINES.

IN FACT, WE'RE GOING TO PARTITION OUR NUMBER LINE INTO SIXTHS SO WE CAN SHOW THE DISTANCES WHERE ALEX STOPPED TO DO CERTAIN ACTIVITIES, SUCH AS TAKING A PICTURE OF A TURTLE.

ARE YOU READY TO HELP ME PARTITION THE NUMBER LINE TO REPRESENT ALEX'S WALK AND THE STOPS THEY TAKE?

GREAT.

EACH PART THAT WE PARTITION THE NUMBER LINE INTO IS CALLED AN "INTERVAL" AND SHOWS A DIFFERENT DISTANCE FROM ZERO AND A DISTANCE TO 1, WHICH WOULD BE THE END OF THE TRAIL.

HMM.

WONDER WHAT FRACTION WE COULD WRITE THAT REPRESENTS THE SAME VALUE OR THE SAME LOCATION ON THE NUMBER LINE AS THE WHOLE NUMBER 0.

WHAT DO YOU THINK?

THAT'S RIGHT.

0 SIXTHS WOULD BE AT THE SAME PLACE AS 0 ON THE NUMBER LINE, BECAUSE ALEX HAS NOT TRAVELED ANY DISTANCE YET.

THE DENOMINATOR OF 6 TELLS US THAT THE DISTANCE OF ALEX'S WALK IS BROKEN UP INTO 6 PARTS, AND THE NUMERATOR OF 0 TELLS US THAT ALEX HAS NOT WALKED ANY OF THOSE PARTS YET.

SO, THE WHOLE NUMBER 0 AND THE FRACTION 0/6 REPRESENTS THE SAME AMOUNT.

IN THIS STORY, 0 AND 0/6 REPRESENTS NO DISTANCE TRAVELED YET.

NOW THAT WE HAVE OUR NUMBER LINE SET UP, LET'S SEE IF WE CAN MARK WHERE ALEX MADE THEIR FIRST STOP.

WHEN ALEX TRAVELED 1/6 OF THE TRAIL, THEY STOPPED AND TOOK A PICTURE OF A TURTLE.

HOW FAR DID ALEX TRAVEL BEFORE STOPPING FOR THE PICTURE?

ALEX TRAVELED 1/6 OF A MILE UNTIL THEY STOPPED.

WE KNOW THE TRAIL'S 1 MILE LONG, AND WE BROKE THE MILE INTO 6 INTERVALS, OR UNITS.

SO FAR, ALEX HAS TRAVELED JUST 1/6 OF A MILE.

IF WE LOOK AT OUR NUMBER LINE, ALEX BEGAN AT 0/6 AND THEN TRAVELED 1/6 OF A MILE BEFORE STOPPING.

IF WE COUNT OUR SIXTHS, WE CAN SEE THAT WE ONLY MADE ONE JUMP ON OUR NUMBER LINE, WHICH MEANS WE ONLY COUNTED ONE SIXTH.

I WONDER HOW MUCH FURTHER ALEX HAS UNTIL THEY REACH THE END OF THE TRAIL?

HOW MANY MORE SIXTHS DO THEY HAVE TO TRAVEL TO REACH THE END OF THE TRAIL?

LET'S COUNT TOGETHER TO FIGURE OUT THE DISTANCE BETWEEN 1/6 AND 1 MILE.

REMEMBER, WE'RE COUNTING SIXTHS, SO WHEN WE COUNT, WE WILL SAY "SIXTH," NOT JUST 1, 2 OR 3.

ARE YOU READY TO COUNT WITH ME?

AWESOME, LET'S GO.

ALEX HAS TO TRAVEL 5/6 MORE TO REACH THE END OF THE TRAIL.

DO YOU THINK 5/6 IS THE SAME VALUE AS 1 WHOLE?

HMM, I HEARD A FEW DIFFERENT RESPONSES, SO, LET'S THINK THROUGH THIS ONE.

THE NUMBER 1 IS A WHOLE NUMBER.

WHEN WE THINK OF THIS RELATED TO FRACTIONS, IF WE HAVE ONE WHOLE, WE'VE COUNTED ALL OF THE PIECES IN OUR WHOLE.

SO, WE NEED TO FIGURE OUT WHAT FRACTION WOULD REPRESENT THE SAME VALUE AS ONE WHOLE MILE AND HAVE A 6 AS A DENOMINATOR.

I HAVE AN IDEA.

WHAT IF WE START AT 0/6 AND COUNT UNTIL WE REACH 1 WHOLE?

COUNT WITH ME.

SO, WHAT FRACTION REPRESENTS THE SAME VALUE AS 1 WHOLE MILE, OR, TO SAY IT IN A DIFFERENT WAY, WHAT FRACTION IS AT THE SAME PLACE ON THE NUMBER LINE AS THE NUMBER 1?

THAT'S RIGHT.

6 SIXTHS IS AT THE SAME PLACE AS 1.

SO, THAT MEANS THAT 6/6 AND 1 HAVE THE SAME VALUE.

SO, IF ALEX TRAVELED 5/6 OF A MILE, WOULD THEY HAVE TRAVELED 1 WHOLE MILE?

NO.

THEY WOULDN'T.

THAT'S RIGHT.

GREAT JOB, EVERYONE.

ACTUALLY, SOMETHING HELPFUL TO KNOW IS, IF THE NUMERATOR AND DENOMINATOR ARE THE SAME NUMBER, THEN THE FRACTION IS EQUAL TO 1.

THE NUMERATOR AND DENOMINATOR ARE THE SAME IN 1 WHOLE, BECAUSE WHEN YOU HAVE 1 WHOLE, YOU'VE COUNTED ALL OF YOUR UNITS.

IN THE EXAMPLE OF 6/6, OUR UNIT IS 6, AND WE HAVE COUNTED 6 OF THOSE SIXTHS, WHICH WOULD BE THE ENTIRE WHOLE.

PRETTY NEAT, HUH?

OKAY, LET'S SEE WHAT ALEX DID NEXT ON THEIR WALK.

ARE YOU READY?

GREAT, LET'S GO.

ALEX STOPPED AGAIN AT 4/6 OF A MILE TO TAKE PICTURES OF SOME TADPOLES.

HAS ALEX TRAVELED 1 MILE YET?

HOW DO YOU KNOW?

NOPE.

REMEMBER THAT THE DENOMINATOR AND NUMERATOR WILL BE THE SAME NUMBER IF A FRACTION IS EQUAL TO 1, BECAUSE WE'VE COUNTED ALL OF OUR UNITS.

SO, ALEX HAS NOT YET WALKED AN ENTIRE MILE.

BUT I WONDER HOW FAR THEY DID WALK.

LET'S FIND OUT.

ALEX HAS ALREADY TRAVELED 1/6 OF A MILE.

WE NEED TO PLACE 4/6 ON THE NUMBER LINE.

LET'S COUNT UNTIL WE REACH 4/6.

REMEMBER, WE'RE STARTING AT 1/6, BECAUSE ALEX HAS ALREADY TRAVELED THAT DISTANCE.

SO, 1/6, 2/6, 3/6.

EXCELLENT COUNTING, MATHEMATICIANS.

WHAT'S THE DISTANCE ALEX TRAVELED WHEN THEY STOPPED TO LOOK AT TADPOLES?

WHAT AMOUNT OF A MILE?

THINK ABOUT HOW MANY JUMPS WE MADE ON THE NUMBER LINE.

WE MADE 3 JUMPS TO GET FROM 1/6 TO 4/6.

WE'RE COUNTING BY SIXTHS, SO WE CAN SAY THAT ALEX TRAVELED 3/6 OF A MILE WHEN THEY STOPPED AGAIN.

EACH OF THOSE JUMPS REPRESENTS 1/6, AND WE MADE 3 OF THOSE JUMPS, SO, WE CAN SEE THAT 1/6 PLUS 1/6 PLUS 1/6 MAKES 3/6.

HOW FAR HAS ALEX TRAVELED SO FAR IN TOTAL?

HOW MUCH OF A MILE?

YES.

IN TOTAL, ALEX HAS TRAVELED 4/6 OF A MILE.

BETWEEN THE FIRST STOP AND SECOND STOP, HOW FAR HAS ALEX TRAVELED?

HOW MANY SIXTHS?

CAN YOU SHOW ME HOW MANY SIXTHS ON YOUR FINGERS?

RIGHT.

BETWEEN THE FIRST AND SECOND STOP, ALEX TRAVELED 3/6 OF A MILE.

YOU ARE ON A ROLL.

LET'S LOOK AT THE LAST ACTIVITY ALEX DID ON THEIR WALK.

AT THE END OF THE MILE, ALEX TOOK A PICTURE OF SOME FISH.

HMM.

WHAT FRACTION WOULD REPRESENT THE END OF THE MILE?

WHAT FRACTION WOULD REPRESENT THE DISTANCE 1 MILE?

AND HERE'S A HINT.

WE TALKED ABOUT THIS EARLIER IN OUR LESSON.

REMEMBER, WHEN ALEX TRAVELED 1/6 OF A MILE AND WE COUNTED THAT THEY WOULD NEED TO TRAVEL 5/6 MORE TO REACH 1 MILE, WE COUNTED FROM 1/6 UNTIL WE REACHED 1 WHOLE.

WHEN WE COUNTED, WE FOUND THAT 6/6 WAS AT THE SAME PLACE AS 1 ON THE NUMBER LINE.

BECAUSE THEY'RE AT THE SAME PLACE, THEY HAVE THE SAME VALUE.

6/6 WOULD BE THE WAY FOR ALEX TO REPRESENT A DISTANCE OF 1 MILE.

IF WE COUNT ON THE NUMBER LINE, WE CAN PROVE THIS, SO, LET'S COUNT.

EXCELLENT COUNTING AGAIN.

ALEX CAN TELL SOMEONE THEY WALKED 1 WHOLE MILE OR 6/6 OF A MILE.

THAT WAS SOME GREAT WALKING AND SOME GREAT PICTURES AND SIGHTS THAT ALEX STOPPED AT ALONG THE WAY.

WHOA.

I JUST FEEL LIKE WE LEARNED SO MUCH TODAY.

I HOPE YOU FEEL THAT WAY, TOO.

THANKS FOR HELPING ME THINK ABOUT THE DISTANCE ALEX WALKED, AND SOME FRACTIONS, TOO.

TODAY, WE LEARNED WHAT THE NUMERATOR AND DENOMINATOR OF A FRACTION REPRESENT AND THAT THEY'RE SEPARATED BY A BAR.

WE ALSO LEARNED THAT WHEN THE NUMERATOR AND DENOMINATOR ARE THE SAME NUMBER, A FRACTION IS EQUAL TO 1, BECAUSE WE'VE COUNTED ALL OF OUR UNITS.

ADDITIONALLY, WE LEARNED HOW TO USE A NUMBER LINE TO REPRESENT FRACTIONS AND THE DISTANCE BETWEEN THEM.

LASTLY, WE LEARNED HOW TO COUNT WITH FRACTIONS WHEN WE DETERMINE THE DISTANCE BETWEEN DIFFERENT NUMBERS.

THANK YOU SO MUCH FOR YOUR HELP.

I'M SO GLAD WE GET TO LEARN ABOUT FRACTIONS TOGETHER.

HERE'S SOMETHING TO THINK ABOUT UNTIL NEXT TIME.

WHAT IF ALEX'S TRAIL WAS PARTITIONED INTO FOURTHS INSTEAD OF SIXTHS?

HOW WOULD THE NUMBER LINE CHANGE?

HOW WOULD YOU KNOW IF ALEX TRAVELED 1 MILE?

I'LL SEE YOU NEXT TIME.

WE'VE BEEN HAVING SO MUCH FUN TODAY LEARNING FROM TEACHERS AND EACH OTHER.

AND NOW, WE HAVE A VERY SPECIAL VIDEO OF SOMEONE ABOUT YOUR AGE READING ONE OF THEIR FAVORITE BOOKS.

I JUST LOVE THIS ONE, AND I KNOW YOU WILL, TOO.

♪ I'M SOPHIA, AND THIS IS NOELLE, AND WE'RE READING "HAIR LOVE."

"MY NAME IS ZURI, "AND I HAVE HAIR THAT HAS A MIND OF ITS OWN.

"IT KINKS, COILS, AND CURLS EVERY WHICH WAY.

"DADDY TELLS ME IT'S BEAUTIFUL.

"THAT MAKES ME PROUD.

I LOVE THAT MY HAIR LETS ME BE ME."

MY TURN TO READ.

"MY..." "IN..." [Noelle] "IN FUNKY BRAIDS WITH BEADS, "I AM A PRINCESS.

"AND WHEN MY HAIR "IS IN TWO PUFFS, "I AM ABOVE THE CLOUDS LIKE A SUPERHERO."

"MY HAIR EVEN DOES MAGIC TRICKS.

[Sophia] "ONE DAY, ROCKY AND I WERE PLAYING OUTSIDE, WHEN ALONG CAME THE RAIN."

[thunder, rain falling] "FROM LARGE TO SMALL IT WENT, PRESTO!

JUST LIKE THAT.

"THERE'S NOTHING MY HAIR CAN'T DO.

"TODAY I WOKE UP EXTRA EARLY, ALL BY MYSELF.

"I WAS TOO EXCITED TO SLEEP.

"IT'S A BIG DAY.

"DADDY WAS STILL SLEEPING.

"'SHH!'

I SAID TO ROCKY AS WE TIPTOED PAST HIM.

LATELY DADDY HAS BEEN WORN OUT."

[father snoring] "HE MAKES ME BREAKFAST, "TAKES ME TO SCHOOL, GOES TO WORK, PICKS ME UP, "AND YESTERDAY, WE WENT FOR A BIKE RIDE AROUND THE PARK.

"I THINK HE NEEDS A BREAK.

"BECAUSE TODAY IS SPECIAL, "I WANT THE PERFECT HAIRSTYLE.

"THIS CALLS FOR A PROFESSIONAL'S TOUCH.

"'PAWS OFF, ROCKY!'

"DADDY HEARD THE CRASH.

"'ZURI, WHAT ON EARTH?'

HE ASKED.

"'I WAS ONLY TRYING TO HELP,' I SAID.

"DADDY SMILED, 'CAN I HELP, TOO?'

"'IT'LL BE A PIECE OF CAKE, ZUZU.'

"THE FIRST STYLE WAS A BIG 'NO WAY.'

"THE SECOND WAS NO BETTER.

'NO, DADDY.'

"THEN DADDY TRIED SLICKING MY HAIR BACK "INTO TWO PUFFS.

"'OUCH!'

DADDY YELLED.

"'WAIT A MINUTE,' DADDY SAID, "AS HE REACHED IN THE DRAWER "AND PICKED OUT A PICK.

"'TA-DA!'

DADDY SAID.

"'DADDY, REALLY?'

I SAID.

"'I'll BE RIGHT BACK,' HE PROMISED.

"'NOW, HOW'S THAT?'

HE ASKED, "PULLING A HAT DOWN OVER MY EYES.

"'DADDY, COME ON, WE CAN DO BETTER THAN THAT.'

"'I REALLY NEED MY HAIR TO BE SPECIAL.'

"'DON'T WORRY,' HE SAID, 'WE'LL FIGURE THIS OUT.'

"AND THEN, I HAD A GREAT IDEA.

"DADDY GATHERED ALL THE TOOLS WE NEEDED, "AND WE WERE SET.

"WATCHING CAREFULLY, DADDY COMBED, PARTED, OILED, TWISTED-- HE NAILED IT."

[applause] "FUNKY PUFF BUNS.

"PRETTY-PRETTY AND SO MUCH FUN.

ROCKY APPROVED, TOO."

[cat meows] "I PUT ON MY SUPERGIRL CAPE "AS THE FINAL TOUCH TO A PERFECT LOOK.

"'WHERE IS MY ZUZU?'

MOMMY CALLED FROM THE DOOR.

"SHE COULD NOT GET IN THE HOUSE FAST ENOUGH.

'MOMMY!'

"'YOU GOTTA BE THE PRETTIEST SUPERGIRL "I HAVE EVER SEEN,' SHE SAID.

"'AND YOUR HAIR IS BEAUTIFUL, ZURI.'

"'WHO DID IT?'

"I LOOKED AT DADDY AND BEAMED.

"MOMMY SMILED.

'VERY NICE .'

"'THANK YOU.

WE LEARNED FROM THE BEST,' DADDY SAID, AS HE GAVE HER A BIG HUG."

[birds singing] [Noelle] "MY HAIR "IS MOMMY, DADDY, AND ME!

IT'S HAIR LOVE!"

THE END.

DID YOU KNOW AN OSTRICH'S EYES IS BIGGER THAN THEIR BRAIN?

YOU KNOW WHAT'S BIGGER THAN YOUR BRAIN?

YOUR BRAIN AFTER THIS MATH LESSON.

LET'S GET INTO IT.

♪ HI, MATHEMATICIANS.

IT'S ME, MS. ALTMAN, AND IT'S AMAZING TO SEE YOU.

BEFORE WE GET STARTED, LET'S TAKE 20 SECONDS TO GRAB SOME SUPPLIES THAT WE WILL NEED FOR OUR TIME TOGETHER TODAY.

YOU WILL NEED PAPER AND A PENCIL.

I'M GOING TO GO AND GET MINE.

WHY DON'T YOU GO AHEAD AND DO THE SAME?

SEE YOU IN A LITTLE BIT.

♪ OKAY, WE'RE BACK, AND OH, MY GOODNESS, LOOK WHERE WE ARE!

WE'RE IN A GROCERY STORE.

AND DO YOU KNOW WHAT?

THE GROCERY STORE MANAGERS HEARD THAT WE ARE AMAZING MATHEMATICIANS, SO THEY ASKED IF WE MIGHT HELP THEM FIGURE OUT HOW TO DISPLAY THE CEREAL INVENTORY ON THEIR SHELVES.

CAN YOU HELP ME?

YOU CAN?

OH, WONDERFUL.

THANK YOU SO MUCH.

I'M WONDERING HOW WE MIGHT INVENTORY ALL OF THESE BOXES OF CEREAL.

DO YOU THINK WE CAN USE A MATH STRATEGY TO HELP US?

YOU DO?

GREAT.

I THINK SO TOO.

TODAY, WE'RE GOING TO LEARN HOW TO USE INVERSE OPERATIONS TO HELP US SOLVE PROBLEMS.

YOU MAY BE THINKING, "WHAT ARE INVERSE OPERATIONS?"

MAKE A PREDICTION ABOUT WHAT YOU THINK INVERSE OPERATIONS MEAN.

TALK TO A FRIEND OR A TRUSTED ADULT.

OH, I HEARD SOMEONE SAY THAT INVERSE OPERATIONS ARE JUST A FANCY WAY OF SAYING "OPPOSITES."

YOU KNOW, LIKE HARD AND SOFT, DRY AND WET, OR COLD AND HOT.

I BET YOU DIDN'T THINK ABOUT THESE THINGS IN MATH AS HAVING OPPOSITES, DID YOU?

WHAT'S THAT?

[laughs] YES, THAT IS TRUE.

I HEARD SOMEONE ASK IF WE COULD EXPLAIN INVERSE OPERATIONS IN ANOTHER WAY, IN A MORE PRECISE, MATH WAY.

ABSOLUTELY.

FOR EXAMPLE, ADDITION AND SUBTRACTION ARE INVERSE OPERATIONS.

LET'S EXPLORE INVERSE OPERATIONS A LITTLE FURTHER BY LOOKING AT SOME EQUATIONS.

WHAT DO YOU NOTICE ABOUT THESE 2 EQUATIONS?

GOOD THINKING.

I HEARD SOMEONE SAY THAT THE 2 EQUATIONS CONTAIN THE SAME NUMBERS.

WHAT ELSE DO YOU NOTICE?

NOT SURE?

OKAY, LET ME HELP YOU OUT.

IN THE FIRST EQUATION, WE STARTED WITH 8 AND ADDED 5 TO IT TO GET TO 13.

IN THE SECOND EQUATION, WE STARTED WITH 13 AND SUBTRACTED 5, AND IT GAVE US 8.

BY SUBTRACTING 5, WE UNDO OUR PREVIOUS ADDITION, OR THE OPPOSITE OF WHAT WE DID IN THE FIRST EQUATION.

SO, TODAY, LET'S USE WHAT WE KNOW ABOUT INVERSE OPERATIONS TO SOLVE MULTIPLICATION AND DIVISION PROBLEMS.

ARE YOU READY?

LET'S JUMP IN.

TAKE THE PROBLEM 45 DIVIDED BY 5, FOR EXAMPLE.

WAIT, WHAT'S THAT?

YOU DON'T WANT TO DO A DIVISION PROBLEM TODAY?

THAT'S OKAY.

REMEMBER, WE'RE USING INVERSE OPERATIONS TODAY.

THE INVERSE OPERATION OF DIVISION IS MULTIPLICATION.

INSTEAD OF DIVIDING, WE CAN USE MULTIPLICATION FACTS.

IS THAT OKAY WITH YOU?

GREAT.

HMM.

WHAT TIMES 5 EQUALS 45?

WHAT'S THAT?

YOU COUNTED BY FIVES ON YOUR FINGERS UNTIL YOU GOT TO 45, AND YOU THINK IT'S 9?

OKAY, LET ME COUNT AGAIN WITH YOU.

YOU READY?

LET'S COUNT BY FIVES USING OUR FINGERS.

5, 10, 15, 20, 25, 30, 35, 40, 45.

HOW MANY FINGERS AM I HOLDING UP?

YES, 9.

YOU WERE CORRECT.

LET'S MAKE AN ARRAY WITH OUR CEREAL BOXES TO CHECK.

SO, 9 x 5 EQUALS 45.

SO, THE INVERSE OPERATION WOULD BE 45 DIVIDED BY 5 EQUALS 9.

LET'S TRY ANOTHER.

LET'S WRITE THIS AS AN INVERSE OPERATION.

ON YOUR PAPER, PLEASE WRITE THE INVERSE OF 32 DIVIDED BY 4.

WHAT DID YOU WRITE ON YOUR PAPER?

SHARE YOUR ANSWER WITH A FRIEND OR TRUSTED ADULT.

VERY GOOD.

YOU WROTE 4 TIMES SOMETHING EQUALS 32.

SO, WE KNOW THAT 4 TIMES SOMETHING EQUALS 32.

DO YOU KNOW A MATH FACT FOR THAT?

YOU DO?

SAY THAT LOUDER.

YES.

4 TIMES 8 EQUALS 32.

OKAY, LET'S BUILD AN ARRAY TO CHECK OUR THINKING.

THAT'S RIGHT, 4 TIMES 8 EQUALS 32, SO 32 DIVIDED BY 4 EQUALS 8.

WOULD YOU LIKE TO TRY ANOTHER ONE?

GREAT.

LET'S TRY A WORD PROBLEM THIS TIME.

I'M GOING TO GIVE YOU A MOMENT TO WORK ON THIS PROBLEM.

YOU READY?

GREAT.

WHAT INFORMATION DO WE KNOW IN THIS PROBLEM?

THAT'S RIGHT.

WE KNOW THAT JAMIE HAS 48 STICKERS.

WHAT ELSE DO WE KNOW?

YES.

HER STICKER BOOK CAN HOLD 8 STICKERS PER PAGE.

HOW CAN WE WRITE THIS INFORMATION AS AN EQUATION?

IF YOU DID NOT WRITE AN EQUATION, PLEASE WRITE ONE DOWN NOW.

ARE YOU READY TO SHARE YOUR EQUATION?

AWESOME SAUCE.

LET'S WRITE AN EQUATION USING THE INFORMATION THAT WE KNOW FROM THE PROBLEM.

JAMIE HAS 48 STICKERS, AND 8 STICKERS CAN GO ON EACH PAGE.

SO, WE CAN WRITE 48 DIVIDED BY 8 EQUALS... SOMETHING.

WHAT'S THAT, MATHEMATICIAN?

YOU WROTE A MULTIPLICATION EQUATION?

YOU WROTE 8 TIMES SOMETHING EQUALS 48?

THAT'S FINE.

YOU WROTE THE INVERSE OF DIVISION, WHICH IS MULTIPLICATION, AND THAT'S OUR STRATEGY FOR TODAY.

SO HOW DID YOU SOLVE THIS PROBLEM?

HOW MANY PAGES WILL SHE NEED?

YES, YOU ARE CORRECT.

SHE WILL NEED 6 PAGES, BECAUSE 6 TIMES 8 EQUALS 48, SO 48 DIVIDED BY 8 EQUALS 6.

LET'S REVIEW.

WE CAN USE THE INVERSE OPERATION, OR MULTIPLICATION, TO SOLVE DIVISION PROBLEMS.

ARE YOU READY TO HELP WITH THE CEREAL DISPLAY?

GREAT.

LET'S DO THIS.

OKAY, MATHEMATICIAN, HOW MANY BOXES OF CEREAL SHOULD WE PUT ON EACH SHELF?

I'M GOING TO GIVE YOU A MOMENT TO WRITE AN EQUATION, THE INVERSE OPERATION, AND TIME TO SOLVE THIS PROBLEM.

♪ ARE YOU READY TO SHARE YOUR THINKING, MATHEMATICIANS?

GREAT.

WHAT IS OUR DIVISION EQUATION TO REPRESENT THIS PROBLEM?

YOU ARE ABSOLUTELY CORRECT.

63 DIVIDED BY 7 EQUALS SOMETHING.

WHAT IS THE INVERSE OPERATION OR MULTIPLICATION EQUATION FOR THIS PROBLEM?

RIGHT AGAIN.

7 TIMES SOMETHING EQUALS 63.

HOW MANY CEREAL BOXES SHOULD WE PUT ON EACH SHELF?

WHAT'S THAT?

OH, NO!

I NEED TO CLARIFY THAT FOR ALL OF OUR MATHEMATICIAN FRIENDS.

ONE OF OUR MATHEMATICIANS MENTIONED THAT THEY KNEW HOW TO WRITE THE EQUATIONS, BUT THEY DIDN'T KNOW WHAT 7 TIMES SOMETHING EQUALS 63, AND THEY NEED OUR HELP.

IT'S OKAY TO ADMIT YOU NEED HELP, BECAUSE WE GROW BY LEARNING FROM OUR MISTAKES.

SO, LET ME CLARIFY.

CREATING A MULTIPLICATION PROBLEM TO SOLVE A DIVISION PROBLEM IS ONE STRATEGY.

IF YOU DON'T KNOW THE MULTIPLICATION FACT JUST LIKE THAT... [snaps fingers] ...YOU CAN USE OTHER STRATEGIES TO HELP YOU, LIKE BUILDING AN ARRAY, MAKING EQUAL GROUPS OR USING SUBTRACTION.

LET'S MAKE EQUAL GROUPS TO HELP SOLVE THIS PROBLEM.

SO, WHAT TIMES 7 EQUALS 63?

MY VISUAL IS USING SHELVES.

THEY ARE PLACING ONE BOX OF CEREAL ON EACH SHELF TO MAKE EQUAL GROUPS.

NOW, LET'S COUNT HOW MANY CEREAL BOXES ARE ON EACH SHELF.

COUNT THE BOXES WITH ME.

1, 2, 3, 4, 5, 6, 7, 8, 9.

THERE ARE 9 CEREAL BOXES ON 7 SHELVES.

SO, 7 TIMES 9 EQUALS 63.

SO, 63 DIVIDED BY 7 EQUALS 9.

GREAT JOB, MATHEMATICIANS.

THANKS FOR JOINING ME TODAY.

I HOPE YOU HAD FUN LEARNING ABOUT INVERSE OPERATIONS AND USING MULTIPLICATION TO SOLVE DIVISION PROBLEMS.

REMEMBER, USING MULTIPLICATION TO SOLVE A DIVISION PROBLEM IS ONLY ONE STRATEGY.

YOU CAN STILL CHECK YOUR WORK BY USING REPEATED SUBTRACTION, BUILDING ARRAYS, OR CREATING EQUAL GROUPS.

JOIN ME NEXT TIME TO LEARN MORE MATH STRATEGIES.

BYE, MATHEMATICIANS!

HI, MY NAME IS ASHLEY, AND I'M AN EDUCATOR HERE AT SYLVAN HEIGHTS BIRD PARK IN SCOTLAND NECK, NORTH CAROLINA.

AND TODAY, I'D LIKE TO INTRODUCE YOU TO ONE OF OUR EDUCATION AMBASSADORS.

THIS IS A HARRIS'S HAWK.

HARRIS'S HAWKS ARE PART OF THE BIRDS OF PREY FAMILY, WHICH ALSO INCLUDES EAGLES, OWLS, AND OSPREY.

THESE BIRDS ALL HAVE A FEW CHARACTERISTICS IN COMMON.

MAINLY, THEY HAVE SOME SHARP, CURVED CLAWS, CALLED "TALONS," USED FOR GRABBING AND GRIPPING THEIR PREY, A SHARP, CURVED, HOOKED BEAK, USED FOR RIPPING AND TEARING THEIR PREY INTO SMALL PIECES TO ALLOW THEM TO EAT IT EASIER, AND THEY USUALLY HAVE MUTED FEATHER COLORS, LIKE BLACKS, BROWNS, GRAYS, AND WHITES.

THERE ARE 17 SPECIES OF HAWKS IN NORTH AMERICA, INCLUDING THE RED-TAILED HAWK AND THE RED-SHOULDERED HAWK, BOTH OF WHICH ARE VERY COMMON IN NORTH CAROLINA AND VIRGINIA.

SO, HARRIS'S HAWKS ARE ACTUALLY NOT NATIVE TO THE EASTERN PART OF THE UNITED STATES.

YOU'LL ACTUALLY FIND THESE ANIMALS LIVING OUT IN THE SOUTHWESTERN PART OF OUR COUNTRY, DOWN INTO MEXICO AND CENTRAL AMERICA.

HARRIS'S HAWKS NORMALLY LIVE IN OPEN, DRY, ARID, KIND OF SCRUB-LIKE HABITATS.

THESE GUYS ARE DESERT-DWELLING HAWKS.

BEING BIRDS OF PREY, HARRIS'S HAWKS PRIMARILY FEED ON SMALL AND MEDIUM-SIZED MAMMALS, OTHER BIRDS, AND REPTILES.

ONE THING THAT SETS OUR HARRIS'S HAWKS APART FROM OTHER BIRDS OF PREY IS THE FACT THAT THEY ARE SOCIAL ANIMALS.

MOST BIRDS OF PREY USUALLY LIKE TO BE SOLITARY.

THEY LIKE TO HANG OUT ON THEIR OWN.

THEY ONLY COME TOGETHER FOR MATING AND NESTING AND TAKING CARE OF THE YOUNG FOR SOME SPECIES.

HARRIS'S HAWKS, ON THE OTHER HAND, DO LIKE TO HANG OUT IN PAIRS OR FAMILY GROUPS.

THEY WILL NEST COMMUNALLY AND ACTUALLY COOPERATE WITH OTHER HARRIS'S HAWKS TO HUNT.

JUST LIKE A PACK OF WOLVES OR A PRIDE OF LIONESSES, HARRIS'S HAWKS WILL WORK TOGETHER TO SORT OF FLUSH OUT, TIRE OUT, AND TAKE DOWN LARGER PREY ANIMALS.

BIRDS OF PREY ARE OFTEN CALLED RAPTORS, COMING FROM THE LATIN WORD "RAPERE," WHICH MEANS "TO GRASP."

AND THAT GOES BACK TO THOSE BEAUTIFUL, REALLY STRONG FEET WITH THOSE CURVED CLAWS, THOSE TALONS, THAT THEY'RE USING TO GRASP THEIR PREY.

THANKS FOR TUNING IN AND JOINING US TODAY.

WE HOPE TO SEE YOU HERE SOON AT SYLVAN HEIGHTS BIRD PARK.

TODAY WAS AMAZING.

AND I'M SO GRATEFUL FOR YOU.

PEACE, A LITTLE BIT OF LOVE, AND A WHOLE LOT OF LEARNING, HOMIES.

BYE.

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